Internal problem ID [5410]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre).
Supplemetary problems. Page 110
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y=\ln \left (x +1\right )^{2}+x -1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve((x+1)^2*diff(y(x),x$2)+(x+1)*diff(y(x),x)-y(x)=(ln(x+1))^2+x-1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-4 x -4\right ) \ln \left (x +1\right )^{2}+2 \left (x +1\right )^{2} \ln \left (x +1\right )+4 c_{2} x^{2}+8 c_{2} x +4 c_{1} +4 c_{2} -3}{4 x +4} \]
✓ Solution by Mathematica
Time used: 0.262 (sec). Leaf size: 72
DSolve[(x+1)^2*y''[x]+(x+1)*y'[x]-y[x]==(Log[x+1])^2+x-1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(-1+2 c_1+2 i c_2) x^2-4 (x+1) \log ^2(x+1)+2 (x+1)^2 \log (x+1)+(-2+4 c_1+4 i c_2) x-1+4 c_1}{4 (x+1)} \]